import numpy as np
import matplotlib.pyplot as plt
from gradient_2d import numerical_gradient

def gradient_descent(f,init_x,lr=0.01,step_num=100):
    x = init_x
    x_history = []

    for i in range(step_num):
        x_history.append(x.copy())

        grad = numerical_gradient(f,x)
        x -= lr*grad 
    return x, np.array(x_history)

def function_2(x):
    return x[0]**2+x[1]**2

init_x = np.array([-3.0,4.0])

lr = 0.1
step_num = 20
x,x_history = gradient_descent(function_2,init_x,lr=lr,step_num=step_num)

plt.plot([-5,5],[0,0],'--b')
plt.plot([0,0],[-5,5],'--b')
plt.plot(x_history[:,0], x_history[:,1], 'o')

plt.xlim(-3.5, 3.5)
plt.ylim(-4.5, 4.5)
plt.xlabel("X0")
plt.ylabel("X1")
plt.show()